I think the case is rare, but I believe it's when the method under test executes entirely in isolation. Put another way, if the method under test doesn't interact in any way with dependent classes or instances, it may be sufficient to Unit test it exclusively.
An example of a method that can execute entirely in isolation is the humanize method defined in rails.
def humanize(lower_case_and_underscored_word)The humanize method is so focused that it manipulates a string and returns the result. I see no need in Functional testing a method that executes at this level of isolation.
lower_case_and_underscored_word.to_s.gsub(/_id$/, "").gsub(/_/, " ").capitalize
Again, I do believe this is rarely the case. Much more often methods interact with instances of other classes (dependencies). Any time you are interacting with dependencies it's important to verify the integration between classes.